1. Field of the Invention
This invention relates to real-time signal processing and more particularly relates to real-time processing of signals representing the complex Kalman filter algorithm.
2. Brief Description of the Prior Art
For years, the Kalman filter has been applied extensively in many signal processing applications, including target tracking, adaptive controls, radar-signal processing, and failure-proof systems. See, for example (1) A. Gebb, Applied Optimal Estimation, The M.I.T. Press, Cambridge, Mass., 1974; (2) J. S. Meditch, Stochastic Optimal Linear Estimation and Control, McGraw-Hill, New York, 1969; (3) H. G. Yeh, "A Design Method for Failure-Proof Systems," Proceedings of the 1983 American Control Conference, San Francisco, Calif., June, 1983, pp. 1219-1223; or (4) H. G. Yeh, Techniques for the Detection, Estimation, Distinction, and Compensation of Failures in Linear Systems, Ph.D. Dissertation, U. C. Irvine, 1982. The applicability of the Kalman filter to real-time signal processing problems is in general limited by the relatively complex mathematical operations necessary in computing the Kalman filtering algorithm. See, for example: (1) H. W. Sorenson, Parameter Estimation, Marcel Dekker, New York, 1980; or (2) A. E. Bryson and Y. C. Ho, Applied Optimal Control, Rev. ed., Halsted Press, Div. of John Wiley & Sons, Waltham, Mass., 1975. The rapid development of VLSI integrated circuits has been reported. See, for example: (1) C. S. Yeh, I. S. Reed, J. J. Chang, and T. K. Truong, "VLSI Design of Number Theoretic Transforms for a Fast Convolution," Proceedings of the 1983 IEEE International Conference on Computer Design: VLSI in Computers, Port Chester, N.Y., Oct. 31-Nov. 3, 1983, pp. 202-203; (2) J. J. Chang, T. K. Truong, H. M. Shao, I. S. Reed, and I. S. Hsu, "The VLSI Design of a Single Chip for the Multiplication of Integers Modulo a Fermat Number," IEEE Trans. on ASSP, Vol. ASSP-33, No. 6, December 1985, pp. 1599-1602; or (3) S. Y. Kung, H. J. Whitehouse, and T. Kailath, VLSI and Modern Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1985, pp. 375-388.
The VLSI development, together with the features of this invention, has made it technologically feasible to implement more complex mathematical relationships, such as the Kalman filter algorithm in real time. A novel method and apparatus for the implementation of this invention does not rely upon the prior art computers for storage, manipulation and nonreal-time solution of the Kalman filter algorithm.